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Q. 49

Expert-verified
Found in: Page 603

### Precalculus Enhanced with Graphing Utilities

Book edition 6th
Author(s) Sullivan
Pages 1200 pages
ISBN 9780321795465

# find the unit vector in the same direction as $v$ $v=3i-4j$

The unit vector in the direction of the vector $v=3i-4j$ is $u=\frac{3}{5}i-\frac{4}{5}j$

See the step by step solution

## Step 1. Given data

The given vector is

$v=3i-4j$

## Step 2. Finding the magnitude of the given vector

The magnitude of the vector $v=3i-4j$ is

$\left|v\right|=\sqrt{{\left(3\right)}^{2}+{\left(-4\right)}^{2}}\phantom{\rule{0ex}{0ex}}⇒\left|v\right|=\sqrt{9+16}\phantom{\rule{0ex}{0ex}}⇒\left|v\right|=\sqrt{25}\phantom{\rule{0ex}{0ex}}⇒\left|v\right|=5$

## Step 3. Finding the unit vector

The unit vector $u$ in the direction of $v$ is:

$u=\frac{v}{\left|\left|v\right|\right|}$

Substitute the values of vector and magnitude vector in the formula.

$u=\frac{3i-4j}{\left|5\right|}\phantom{\rule{0ex}{0ex}}⇒u=\frac{3}{5}i-\frac{4}{5}j$